Managers need to justify their jobs. Reading off a slack report every day seems too simple and not worthy the salary they're paid. Compare that to a large meeting and live status updates, everyone stands, etc. Now that is some "serious work" happening.
Think of it from the point of view that managers have mangers they report to. When shit goes wrong they have to cover their asses. "So it's late. But did you check on their progress? Wait just over slack, no actual meetings? Ok, that obviously needs improvement".
It's not like it's a requirement that "managers" be at a standup meeting. Some of the best teams I've worked on have done daily standups without managers, and I dare to say most of us enjoyed them and found them productive!
Managers are often looking for ways to fill their calendar. Meetings, calls that could be a two-minute Slack exchange, et c. Some will hop into meetings like that if they can. They love the recurring ones, especially, bonus if they can apologize any time they have to skip it for something that actually, maybe, matters ("uh, yeah, we don't care if you come, OK, thanks for apologizing I guess?")
I have never been in a team where managers were present at the standup meeting. In fact, sometimes I have no idea who my "manager" even is. We've got a team, we've got stakeholders, we do the work. If a manager wants to join, that's fine, but he's not in charge of that meeting.
All this talk of standup meetings being primarily for managers is really weird. It's not for managers, and they have no reason to be present. It's for the team, to improve cooperation within the team. If the team has a better way to accomplish that, then they should use that.
Think of it from the point of view that managers have mangers they report to. When shit goes wrong they have to cover their asses. "So it's late. But did you check on their progress? Wait just over slack, no actual meetings? Ok, that obviously needs improvement".